In what ways does Macbeth attempt to control the future and bury the past?

After Duncan names his older son, Malcolm, the Prince of Cumberland, we see Macbeth begin to plot to control the future.  He says to himself,

The prince of Cumberland!  That is a step
On which I must fall down, or else o'erleap,
For in my way it lies.  Stars, hide your fires;
Let not light see my black and deep desires (1.4.50-53).

Macbeth means that—now that Malcolm is Duncan's official heir—Macbeth is going to have to find a new way to become king.  He is going to have to go over Malcolm or stop here.  He, of course, decides to jump over this step; he asks the stars to go dark so that no one will be able to see his dark ambitions and plans.  In this way, he attempts to control the future, impeding Malcolm's progress to the throne while opening up his own path.

Macbeth also attempts to bury the past when he murders Duncan's chamberlains, the two men that he and Lady Macbeth successfully framed for the king's murder.  After he returns from seeing Duncan's dead body with the nobles who have come to awaken the king, he says, 

Oh, yet I do repent me of my fury,
That I did kill them  (2.3.84-85).

By killing the only individuals that could identify him as the king's killer—aside from his wife—Macbeth buries the past.  

Macbeth tries to further control the future when he orders the murders of Banquo and his son, Fleance.  The Weird Sisters originally told Banquo, 

Thou shalt get kings, though thou be none  (1.3.68).

In other words, though Banquo himself will never be king, the witches tell him that his descendants will be kings.  In an effort to control the future, Macbeth hires men to murder Banquo, so he cannot father additional children. He also tells the men to kill Fleance so that he can never become king or father kings.  As he tells the murderers,

Fleance, [Banquo's] son, that keeps him company,
Whose absence is no less material to me 
Than is his father's, must embrace the fate
Of that dark hour (3.1.140-143).

Macbeth tries to control the future by eliminating any possibility that the throne could go to someone in Banquo's family line.  Unfortunately for him, the murderers fail to kill Fleance, and he must continue to worry about the future the Weird Sisters predicted.